To determine the whole number unknowns for a solution set given the graph of an inequality in two variables (like \(x < y\)), we need to analyze the graph's characteristics:
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Identify the Line: The inequality is typically represented by a boundary line, which corresponds to the equation derived from the inequality. For example, \(x < y\) corresponds to the line \(x = y\).
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Determine the Type of Inequality: Since the inequality is strict (\(<\)), the line itself will not be included in the solution set. The area you are interested in would be either above the line \(x = y\) or below it, depending on whether the inequality was \(x < y\) or \(x > y\).
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Determine the Region: For \(x < y\), the solution set consists of all points that lie below the line \(x = y\). That is, any point \((x, y)\) satisfying the condition \(y > x\).
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Identify Whole Number Solutions: The "whole number unknowns" refer to integer solutions \((x, y)\) where both \(x\) and \(y\) are whole numbers (non-negative integers: \(0, 1, 2, 3, \ldots\)).
For the inequality \(x < y\):
- Possible Pairs:
- If \(x = 0\), then \(y\) can be \(1, 2, 3, \ldots\) (all integers greater than 0).
- If \(x = 1\), then \(y\) can be \(2, 3, 4, \ldots\) (all integers greater than 1).
- If \(x = 2\), then \(y\) can be \(3, 4, 5, \ldots\) (all integers greater than 2).
- This pattern continues for larger values of \(x\).
So, for each whole number \(x = n\), \(y\) must be chosen from the set of numbers greater than \(n\).
- Conclusion: The solution set in whole numbers for the inequality \(x < y\) consists of pairs \((x, y)\) where \(y\) is always one whole number greater than \(x\) or more, such as:
- \((0, 1), (0, 2), (0, 3), \ldots\)
- \((1, 2), (1, 3), (1, 4), \ldots\)
- \((2, 3), (2, 4), (2, 5), \ldots\)
- and so forth.
The valid pairs form a triangle below the diagonal line \(x = y\) in the first quadrant, starting from the origin.
If you need specific integer pairs or have a particular graph in mind, please provide more detail, or you can work with the outlined method to find the solutions based on the graph.